Question

$\overline{qr}$, $\overline{rs}$, and $\overline{sq}$ are midsegments of $\triangle wxy$.
$qr = 2.93$ cm
$rs = 2.04$ cm
$qs = 2.28$ cm
what is the perimeter of $\triangle wxy$?
14.50 cm
11.57 cm
12.46 cm
12.22 cm

Explanation:

Step1: Recall Midsegment Theorem

The midsegment of a triangle is parallel to the third side and half as long. So, each side of $\triangle WXY$ is twice the length of the corresponding midsegment.

Step2: Find lengths of $\triangle WXY$ sides

• Side opposite $QR$: $2\times QR = 2\times2.93 = 5.86$ cm
• Side opposite $RS$: $2\times RS = 2\times2.04 = 4.08$ cm
• Side opposite $QS$: $2\times QS = 2\times2.28 = 4.56$ cm

Step3: Calculate perimeter

Perimeter = sum of all sides = $5.86 + 4.08 + 4.56$ = $14.50$ cm

Answer:

14.50 cm